单周期通顿的分析

Q3 Social Sciences Social Security Bulletin Pub Date : 2016-11-09 DOI:10.2139/ssrn.2874160
Michael J. Sabin, J. Forman
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引用次数: 13

摘要

单期投资是一种安排,一组成员向一个投资池缴款,在一段固定的时间后,该投资池将分配给那些仍然活着的成员。根据成员的死亡概率和贡献金额进行不相等的分配。在一篇配套文章中,我们应用单周期时间来提出我们认为具有商业潜力的产品。在这里,我们关注的是分析。这一分析不仅适用于单期投资,也适用于其他可以作为单期投资序列进行分析的安排,例如集合年金基金。本文的核心是发展幸存成员在单周期内随机接收量的均值和方差的公式。我们使用这些公式来解决一个关于集中年金基金偏差的公开问题,并展示在哪些实际条件下偏差可以忽略不计。我们将展示提供者如何使用公式来管理订阅过程,确定允许谁参与以及允许他们贡献多少,以便对tontine的统计数据进行有利的控制。我们使用这些公式来比较在单个队列中混合不同的队列与为每个队列创建单独的队列,发现混合队列更好,因为它降低了特异性风险和系统风险。
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The Analytics of a Single-Period Tontine
A single-period tontine is an arrangement in which a group of members contribute to an investment pool, and after a fixed period of time, the pool is distributed to those members who are still alive. The distribution is made in unequal amounts based on member death probabilities and contribution amounts. In a companion article we apply the single-period tontine to propose products that we feel have commercial potential. Here, we focus on the analytics. The analysis applies not just to single-period tontines, but also to other arrangements that can be analyzed as a sequence of single-period tontines, such as pooled annuity funds.The core of the paper is the development of formulas for the mean and variance of the random amount that a surviving member receives in a single-period tontine. We use the formulas to resolve an open question about bias in pooled annuity funds and to show practical conditions under which it can be made negligible. We show how the provider can use the formulas to manage the subscription process, determining who is allowed to participate and how much they are allowed to contribute, so that the statistics of the tontine are favorably controlled. We use the formulas to compare mixing different cohorts within a single tontine versus creating a separate tontine for each cohort, finding that mixing cohorts is better because it reduces both idiosyncratic risk and systematic risk.
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来源期刊
Social Security Bulletin
Social Security Bulletin Social Sciences-Social Sciences (miscellaneous)
CiteScore
0.70
自引率
0.00%
发文量
0
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